Title: Large gauge hierarchy in gauge-Higgs unification

Abstract

We study a five dimensional SU(3) nonsupersymmetric gauge theory compactified on M{sup 4}xS{sup 1}/Z{sub 2} and discuss the gauge hierarchy in the scenario of the gauge-Higgs unification. Making use of the calculability of the Higgs potential and a curious feature that coefficients in the potential are given by discrete values, we find two models, in which the large gauge hierarchy is realized, that is, the weak scale is naturally obtained from a unique large scale such as a grand unified theory scale or the Planck scale. The size of the Higgs mass is also discussed in each model. One of the models we find realizes both large gauge hierarchy and consistent Higgs mass, and shows that the Higgs mass becomes heavier as the compactified scale becomes smaller.

@article{osti_21011108,
title = {Large gauge hierarchy in gauge-Higgs unification},
author = {Sakamoto, Makoto and Takenaga, Kazunori},
abstractNote = {We study a five dimensional SU(3) nonsupersymmetric gauge theory compactified on M{sup 4}xS{sup 1}/Z{sub 2} and discuss the gauge hierarchy in the scenario of the gauge-Higgs unification. Making use of the calculability of the Higgs potential and a curious feature that coefficients in the potential are given by discrete values, we find two models, in which the large gauge hierarchy is realized, that is, the weak scale is naturally obtained from a unique large scale such as a grand unified theory scale or the Planck scale. The size of the Higgs mass is also discussed in each model. One of the models we find realizes both large gauge hierarchy and consistent Higgs mass, and shows that the Higgs mass becomes heavier as the compactified scale becomes smaller.},
doi = {10.1103/PHYSREVD.75.045015},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

In this paper we increase the minimal supersymmetric standard model tree level Higgs mass bound to a value that is naturally larger than the LEP-II search constraint by adding to the superpotential a {lambda}SH{sub u}H{sub d} term, as in the next to minimal supersymmetric standard model, and UV completing with new strong dynamics before {lambda} becomes nonperturbative. Unlike other models of this type, the Higgs fields remain elementary, alleviating the supersymmetric fine-tuning problem while maintaining unification in a natural way.

We derive an useful formula by which the effective potential of the Higgs field is easily calculated in the gauge-Higgs unification scenario in the warped background. This scenario has many interesting features and attracts attentions in these days. One of the peculiar predictions is the relatively large Higgs mass. However, the effective potential of the Higgs field, which determines the Higgs mass, has not been investigated so much. The formula which we derive here will be helpful for this purpose. As an application, we investigate the gauge-Higgs condition that the effective theory of the gauge-Higgs unification model should satisfy.

We study an SU(2) supersymmetric gauge model in a framework of gauge-Higgs unification. Multi-Higgs spectrum appears in the model at low energy. We develop a useful perturbative approximation scheme for evaluating effective potential to study the multi-Higgs mass spectrum. We find that both tree-massless and massive Higgs scalars obtain mass corrections of similar size from finite parts of the loop effects. The corrections modify the multi-Higgs mass spectrum, and hence, the loop effects are significant in view of future verifications of the gauge-Higgs unification scenario in high-energy experiments.

We evaluate the radion and Higgs masses in the gauge-Higgs unification models on the warped geometry, in which the modulus is stabilized by the Casimir energy. We analyze the one-loop effective potential and clarify the dependences of those masses on the Wilson line phase {theta}{sub H}. The radion mass varies 1-30 GeV for 0.06{<=}sin{theta}{sub H{<=}}0.3, while the Higgs mass is 150-200 GeV and depends on {theta}{sub H} only logarithmically. The radion couplings to the standard model particles are sensitive to the warp factor, and are too small to detect at colliders in the region where the five-dimensional description is valid.